Is this the one?
(There is a CD player hidden behind the "Technics Tower" label).
More info if that is it:
http://www.foundvalue.com/photo/technics-home-audio-shelf-system-with-turntable-7751
PS - I am not familiar with this so cannot comment; however, you did not give enough info for us to help you.
Also, be specific, what is a "very reasonable" price? For $100, if everything works and you are pleased with the sound, go for it.
At some point Technics went from being "Upscale Panasonic" to a non-entity in the audio sector. Depending when that was, this could be a fairly competent system (but not anything to get excited about) or a glorified boombox repackaged in separate over-sized boxes to look like a legit system.
I did see the speakers being sold separately for $129/pr on ebay FWIW. Unfortunately, I have seen some pretty crappy stuff being designated as "vintage" with a price tag that is a total rip-off, so I would not put too much stock in that.
If you are not familiar with Vinyl, I would comment that you don't want to get into it on a limited budget. Likely this turntable/stylus will damage your records. Even if the turntable turns out to be good (and Technics did maker some good turntables),chances are the stylus is in poor condition. I'd hate to see you buy this and build up a record collection only to find that your records no longer sounded very good once you replaced it with a nicer system.
One reasonable test for quality is the weight of the amp. as a Class A amp, it should be heavy if it is a quality unit.
Also make sure there is no scratchy noise when you adjust the volume, bass, or treble knobs and that the surrounds of the speakers (the outer-most hump around the circumference of the speaker drivers).
Good luck!